控制理论与应用2024，Vol.41Issue(7)：1172-1180,9.DOI:10.7641/CTA.2024.30501
公理化的矩阵半张量积
Axiomatized semi-tensor product of matrices
摘要
Abstract
An axiomatic framework is provided for the semi-tensor product(STP)of matrices,which consists of three kinds of STPs:matrix-matrix STP,matrix-vector STP and vector-vector STP.First,several commonly used STPs are surveyed with their basic properties and applications.Then,a newly appearing STP,called the dimension keeping STP,is introduced.The dimension keeping STP is a multi-functional STP,which can realize the functions of the matrix-matrix STP,matrix-vector STP,and vector-vector STP simultaneously.Finally,this paper also briefly introduces some algebraic properties brought by the dimension keeping STP,including Cayley-Hamilton theory of non-square matrices,eigenvalue and eigenvector of non-square matrices.关键词
公理化的矩阵半张量积/超矩阵/保维数矩阵半张量积/非方矩阵的Cayley-Hamilton定理Key words
axiomatized semi-tensor product/hypermatrix/dimension keeping semi-tensor product/Cayley-Hamilton theory of non-square matrices引用本文复制引用
程代展,赵荣,冯俊娥..公理化的矩阵半张量积[J].控制理论与应用,2024,41(7):1172-1180,9.基金项目
国家自然科学基金项目(62350037,62073315,62273201,12326425),山东省泰山学者特聘教授基金项目(TSTP20221103)资助.Supported by the National Natural Science Foundation of China(62350037,62073315,62273201,12326425)and the Research Fund for the Taishan Scholar Project of Shandong Province(TSTP20221103). （62350037,62073315,62273201,12326425）
